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On degree-based topological indices of random polyomino chains
Saylé C Sigarreta1, Saylí M Sigarreta1, Hugo Cruz-Suárez1
1Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Ave. San Claudio y Río Verde, Col. San Manuel, CU, Puebla 72570, Puebla, Mexico.
Mathematical Biosciences and Engineering : MBE
|August 9, 2022
Summary
This study analyzes degree-based topological indices in random polyomino chains using a martingale approach. We determined their asymptotic distribution, expected values, and variances, confirming known results and calculating new ones.
Area of Science:
- Chemical graph theory
- Combinatorics
- Probability theory
Background:
- Topological indices quantify molecular structure.
- Polyomino chains are complex graph structures.
- Understanding their properties is crucial in cheminformatics.
Purpose of the Study:
- To compute degree-based topological indices in random polyomino chains.
- To derive the asymptotic distribution, expected value, and variance using a martingale approach.
- To calculate expected values for specific indices like Sombor, Forgotten, and Zagreb.
Main Methods:
- Martingale approach for probabilistic analysis.
- Asymptotic distribution calculations.
- Computation of expected values and variances for topological indices.
Main Results:
- The asymptotic distribution, expected value, and variance of degree-based topological indices in random polyomino chains were obtained.
- Several known results for polyomino chains were re-derived as corollaries.
- Expected values for Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randić, and geometric-arithmetic indices were computed.
Conclusions:
- The martingale approach provides a robust framework for analyzing topological indices in random polyomino chains.
- The derived results offer valuable insights for applications in chemical graph theory and related fields.
- This work extends the understanding of topological indices in complex molecular structures.
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